Electron-phonon drag ( Eng. Electron-phonon drag ) - interaction with nonequilibrium phonons of current carriers ( electrons or holes ) in a conductor. When a temperature gradient is created in a sample, a phonon flux arises, which scatters on the electrons and gives them part of its quasimomentum and creates a flux of them from the hot to cold edge of the sample. This is one of the contributions to the thermoelectric effect in a closed circuit. In an open circuit, the thermoelectric power of entrainment occurs. The drag effect was predicted by L. E. Gurevich for metals in 1945 [1] [2] . Fredericks first observed this effect in Germany in 1953 [3] . The effect is observed in fairly pure samples with a mean free path of the current carriers comparable to phonons, that is, the electron-phonon interaction is the main scattering mechanism of current carriers, not impurities and other relaxation processes [4] , and makes the main contribution to the thermopower at low temperatures .
General equations
For a three-dimensional crystal with a cubic lattice , the dispersion laws for electrons, acoustic and optical phonons are written in the form:
where p is the electron quasimomentum, q is the phonon quasimomentum ( q = | q |), m is the effective mass of the electron, α is the dispersion constant, a is the lattice constant, Is the reduced Planck constant, ω and Ω are the frequencies of acoustic and optical phonons. The kinetics of quasiparticles is described by nonequilibrium distribution functions for electrons - f , acoustic and optical phonons - N and N o . These functions satisfy the associated Boltzmann kinetic equations:
- ,
- ,
- {\ displaystyle {\ frac {\ partial N ^ {o}} {\ partial t}} + {\ textbf {v}} _ {q} ^ {o} \ cdot \ nabla N ^ {o} = S_ {oe } + S_ {oo} + S_ {od} + S_ {op}} ,
- ,
where r is the coordinate (radius vector), t is time, v , v q and v q o are the velocities of the electron, acoustic and optical phonons. E is the electric field, H is the magnetic field strength , c is the speed of light, S with indices is the collision integral where the first indices denote the scattered particle, and the second the scatterer. e, p, o, and d correspond to electrons, acoustic phonons, optical phonons, and defects such as impurities and sample boundaries. In general terms, the problem reduces to solving these equations under some assumptions (simplifications) in the form of collision integrals.
Notes
- ↑ LE Gurevich. // Zh. Eksp. Teor. Fiz .. - 1946. - S. 193 .
- ↑ LE Gurevich. // Zh. Eksp. Teor. Fiz .. - 1946 .-- S. 416 .
- ↑ HPR Frederikse. Thermoelectric Power of Germanium below Room Temperature // Phys. Rev .. - 1953. - T. 92 . - S. 248 . - DOI : 10.1103 / PhysRev . 92.248 .
- ↑ Yu. G. Gurevich, OL Mashkevich. Electron-phonon drag and transport phenomena in semiconductors // Physics Rep .. - 1989. - T. 181 . - S. 327—394 . - DOI : 10.1016 / 0370-1573 (89) 90011-2 .